2009/12/17 by Max-Albert Knus, Jean-Pierre Tignol, Knus, Max-Albert +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.0912.3359
arxiv created 2009/12/17 · openalex publication_date 2009/12/17 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Severi-Brauer varieties are twisted forms of projective spaces (in the sense of Galois cohomology) and are associated in a functorial way to central simple algebras. Similarly quadrics are related to algebras with involution. Since thin projective spaces are finite sets, thin Severi-Brauer varieties are finite sets endowed with a Galois action; they are associated to etale algebras. Similarly, thin quadrics are etale algebras with involution. We discuss embeddings of thin Severi-Brauer varieties and thin quadrics in Severi-Brauer varieties and quadrics as geometric analogues of embeddings of etale algebras into central simple algebras (with or without involution), and consider the geometric counterpart of the Clifford algebra construction.